Bullying from unqualified teacher

Basically you are paying for what the school got when they decided to employ an unqualified teacher - a lack of professionalism. Threaten to start a grievance procedure against her and make the SMT aware that you want something done now about this persons unprofessional behaviour.

You have to assert yourself and tackle the rudeness. Arrange a meeting and discuss with her the concept of constructive polite criticism. Make it clear that you will only engage with ideas/suggestions which are the result of reasoned/reasonable debate.